Problem: Simplify the following expression: $ a = \dfrac{-3n - 7}{-8n - 2} + \dfrac{-8}{3} $
Explanation: In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{3}{3}$ $ \dfrac{-3n - 7}{-8n - 2} \times \dfrac{3}{3} = \dfrac{-9n - 21}{-24n - 6} $ Multiply the second expression by $\dfrac{-8n - 2}{-8n - 2}$ $ \dfrac{-8}{3} \times \dfrac{-8n - 2}{-8n - 2} = \dfrac{64n + 16}{-24n - 6} $ Therefore $ a = \dfrac{-9n - 21}{-24n - 6} + \dfrac{64n + 16}{-24n - 6} $ Now the expressions have the same denominator we can simply add the numerators: $a = \dfrac{-9n - 21 + 64n + 16}{-24n - 6} $ $a = \dfrac{55n - 5}{-24n - 6}$ Simplify the expression by dividing the numerator and denominator by -1: $a = \dfrac{-55n + 5}{24n + 6}$